SOLUTION: Please help factor by grouping: p^2 - q^2 + r^2 - 2pr This is straight from book. Thanks for showing steps.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help factor by grouping: p^2 - q^2 + r^2 - 2pr This is straight from book. Thanks for showing steps.      Log On


   

Question 385283: Please help factor by grouping:
p^2 - q^2 + r^2 - 2pr
This is straight from book.
Thanks for showing steps.
Found 2 solutions by mananth, jim_thompson5910:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
p%5E2+-+q%5E2+%2B+r%5E2+-+2pr
..
reorganize the terms
p%5E2-2pr%2Br%5E2+-q%5E2
...
%28p-r%29%5E2-q%5E2
...
%28p-r%2Bq%29%28p-r-q%29
...
m.ananth@hotmail.ca

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
p%5E2+-+q%5E2+%2B+r%5E2+-+2pr Start with the given expression.


p%5E2+-+2pr+%2B+r%5E2+-+q%5E2++ Rearrange the terms.


%28p-r%29%5E2+-+q%5E2++ Factor p%5E2+-+2pr+%2B+r%5E2 to get %28p-r%29%5E2


%28p-r%2Bq%29%28p-r-q%29++ Now use the difference of squares formula to factor.


So p%5E2+-+q%5E2+%2B+r%5E2+-+2pr factors to %28p-r%2Bq%29%28p-r-q%29++


In other words, p%5E2+-+q%5E2+%2B+r%5E2+-+2pr=%28p-r%2Bq%29%28p-r-q%29++